$($b$)$ Let

$I={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\sqrt[\phantom{2}]{1\frac{1}{x^2}}dx$

$($i$)$ Make the substitution $u=\sqrt[\phantom{2}]{x^{2}1}$ to express I as an integral of $u.$

$($ii$)$ Solve the resulting integral.